We did. American speech is based on British accents of the 17th and 18th century. What is now known as a 'British accent' was developed in the early 19th century.
Of course, if you listen carefully, some things change every 30-40 years. You won't hear a trace of t-glottalization in British speech of the 1950s. On the other hand, nobody drops the 'h' any more.
Do you ever notice that Americans say "I don't have" and Brits always say "I haven't got." Explain that one. I've also noticed that Britons never use "gotten." Americans still do. A retention of the Germanic ending that Great Britain dropped years ago? I think we also use "oxen" as the plural and I don't think British English does. I may be wrong .... Anyway, it's all very interesting to this English major (B.A., cum laude).